Detailed descriptions of radio networks and systems can be found in literature, such as in Technical Specifications published by, e.g., the 3rd Generation Partnership Project (3GPP). In such systems, user equipments (UE) can, e.g., access mobile services via an access network comprising a Radio Access Network (RAN) and a Core Network (CN). Examples of 3GPP-based communication networks include, for example, 2G GSM/GPRS (Global System for Mobile Communications/General Packet Radio Services), 3G UMTS (Universal Mobile Telecommunications System), and LTE (Long Term Evolution) EPS (Evolved Packet System). Examples of radio access networks (RAN) include GERAN (GSM/EDGE (Enhanced Data rates for GSM Evolution) RAN for 2G GSM/GPRS), UTRAN (Universal Terrestrial RAN for 3G UMTS), and E-UTRAN (Evolved UTRAN for LTE EPS). Examples of packet core networks include GPRS Core (for 2G and 3G) and Evolved Packet Core (for 2G, 3G UTRAN and E-UTRAN).
A fundamental requirement for a radio network is the possibility for a UE to request a connection setup to the radio network. This is commonly referred to as random access. FIG. 1 illustrates an example random access procedure of a UE in a 3rd Generation Partnership Project (3GPP) Long Term Evolution (LTE) communication system. In LTE, random access is used for several purposes, including among other things:                for initial access when establishing a radio link (moving from a RRC_IDLE state to a RRC_CONNECTED state; RRC is an abbreviation for Radio Resource Control);        for re-establishing a radio link after radio link failure;        for handover when uplink synchronization is to be established to a new radio cell;        for establishing uplink (i.e. the direction from UE to radio network) synchronization if uplink (UL) or downlink (DL) data arrives when the UE is in the RRC_CONNECTED state and the UL is not synchronized;        for the purpose of positioning using positioning methods based on UL measurements;        as a scheduling request if no dedicated scheduling-request resources have been configured on the Physical Uplink Control Channel (PUCCH).        
Acquisition of UL timing is an objective for all cases above. When establishing an initial radio link (i.e., when the UE is moving from RRC_IDLE to RRC_CONNECTED), the random access procedure generally also serves the purpose of assigning a unique identity, namely the Cell Radio Network Temporary Identifier (C-RNTI), to the UE. There are two types of random access schemes, a contention-based random access and a contention-free random access.
An example of contention-based random access procedure using a four-step procedure, illustrated in FIG. 1, comprises the following steps:                Step 101. The UE 10 transmits 101 a random access preamble (RA MSG1) to the radio network node 20, e.g., on the Physical Random Access Channel (PRACH).        Step 102. The radio network node 20 transmits 102 a random access response (RAR) RA MSG2 to the UE 10. With reference to FIG. 2, an example of a RAR message (i.e. RA MSG2 transmitted 102 from the radio network node 20 to the UE 10) is shown. A medium access control (MAC) protocol data unit (PDU) format as defined in the Technical Specification 3GPP TS 36.321 V.11.2.0 (see e.g. chapter 6.1.5 “MAC PDU (Random Access Response)”) and as exemplified in FIG. 2 comprises a MAC header 230 and zero, one or more MAC RARs 240. The MAC RARs 240 are so-called payload fields. Optionally, a padding field 250 can be included. The MAC header 230 has a variable length and includes at least one MAC subheader 210, 220. Each subheader 220 except a Backoff (BI) indicator subheader 210 corresponds to one MAC RAR. If included, the BI subheader 210 may be the first subheader included within the MAC header 210. According the earlier-mentioned technical specification, i.e. 3GPP TS 36.321 V11.2.0 (see e.g. chapter 6.1.5 “MAC PDU (Random Access Response)”), and as exemplified in FIG. 3 a MAC RAR 240 generally comprises four fields 310-340. Each MAC RAR generally comprises six octets, each octet comprising eight bits. A first field 310 is a reserved (R) field of one bit. A second field 320 is a Timing Advance Command field of eleven bits. A third field 330 is an uplink (UL) grant field. The third field 330 is generally 20 bits. Finally, a fourth field 340 is a Temporary C-RNTI (Cell Radio Network Temporary Identifier) field. The fourth field 340 is generally 16 bits.        Step 103. When the UE 10 successfully receives a response message, RA MSG 2, from the radio network node 20 (i.e. in response to the random access preamble sent in RA MSG 1), the UE 10 transmits RA MSG3 including a UE identifier (ID) to the radio network node 20. When doing so, the UE 10 may use radio resources which have been allocated to the UE 10 by the radio network node 20, as is well-known among persons skilled in the art. The RA MSG 3 is sometimes referred to as a RRCConnectionRequest message.        Step 104. The radio network node 20 receiving the RA MSG 3 transmits 104 a RA MSG 4 to complete, or conclude, the contention resolution. This RA MSG4 is sometimes referred to as a RRCConnectionSetup message. Consequently, the UE 10 receives the contention resolution message RA MSG 4. The random access procedure is completed when the UE 10 receives the contention resolution message RA MSG 4.        
It should be appreciated that contention-free random access is generally only used for re-establishing UL synchronization upon DL data arrival, handover and positioning. Only the first two steps, i.e. steps 101-102, of the procedure in FIG. 1 are used as there is generally no need for contention resolution in a contention-free random access. A more detailed description of the random access procedures in general can be found in literature, such as in the reference book 4G LTE/LTE-Advanced for Mobile Broadband by Erik Dahlman, Stefan Parkvall and Johan Sköld, Academic Press, 2011, ISBN:978-0-12-385489-6, see e.g. chapter 14.3 “Random Access”.
The number of UEs such as mobile telephones, cellular telephones, laptops, or tablet computers is increasing rapidly. At the same time, the number of Machine Type Communication (MTC) devices (see e.g. 3GPP TS 22.368 V.12.0.0) in radio networks is increasing rapidly too. MTC devices are a form of a UE which does not necessarily involve human interaction and may, e.g., include sensors, actuators, measurement devices, etc. A potential challenge when the number of UEs (including MTC devices) is increasing rapidly is that that more UEs may request radio network resources simultaneously. As a consequence, the demand from UEs for initiating random access procedures also increases. In turn, the risk for congestion or overload in radio networks increases.